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We prove that if $S+\\lambda_2$ is constant and larger than $2$, then $S+\\lambda_2\\geq3$. Thus Lu's second-gap conjecture holds for minimal surfaces in codimension two.\n  Together with the hypersurface result of Peng--Terng and the counterexamples of Li--Zhao in every codimension $m\\geq3$, our theorem completes the codimension picture of Lu's second-gap conjecture for minimal surfaces: it holds precisel","authors_text":"Fagui Li, Jianquan Ge, Yunheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-23T14:05:10Z","title":"Lu's conjecture for minimal surfaces in codimension two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21336","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:62f719cef139adcd379ca835b8b51c99fe48b51bfdd2a93e823084773700ce9c","target":"record","created_at":"2026-07-24T01:24:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"93081ce769220b77bb8ed57107b01751bb6c24de9f02eeac6b893ccb200ac0f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-23T14:05:10Z","title_canon_sha256":"07396daa8b9eb2860e571ddc6f9785c1895aa42495dac75c9f0bbcf6fa5d2425"},"schema_version":"1.0","source":{"id":"2607.21336","kind":"arxiv","version":1}},"canonical_sha256":"99f5caa505f5f2afc28719fd22ab502e571bfc242d3089253b5d7c6481dceb54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99f5caa505f5f2afc28719fd22ab502e571bfc242d3089253b5d7c6481dceb54","first_computed_at":"2026-07-24T01:24:26.446759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-24T01:24:26.446759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bkN1i3TPqlP+dEfEL75dySLXaVTBORzqeQFDUgO04zzvQQZuCLL5/qymk1uZEeDYTlDaAM9vMJvJOyUPd91FBA==","signature_status":"signed_v1","signed_at":"2026-07-24T01:24:26.447658Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21336","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62f719cef139adcd379ca835b8b51c99fe48b51bfdd2a93e823084773700ce9c","sha256:01643fc59fc02c34359e8a67a6cf32593dfb63c955e87bcb9900d1af8e029710"],"state_sha256":"74432acd954bd0b93b72f20dbf057a9024accf2ff58eb11a59a9736424d2adf9"}